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From: paul c <toledobythesea@ooyah.ac>
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Subject: Re: RM and abstract syntax trees
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Date: Wed, 31 Oct 2007 00:24:00 GMT
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Bob Badour wrote:
> paul c wrote:
> 
>...
>> Here's my favourite nested relation, although I admit it's probably 
>> useless in practice.  It's a recursive one.  Sorry I don't have much 
>> mastery of conventional syntax, what I mean here is something like R: 
>> <attribute list> where <attribute list> is a set of attribute name, 
>> attribute type pairs and typeof is swiped from C-language:
>>
>> R: (A typeof R)
>>
>> I don't know how to display a value for R but I guess it could have 
>> either no tuples or one tuple.
> 
> It could have any number of tuples. See formalism under "philosophy of 
> mathematics".
> 
> Example values are:
> zero tuples:
> {}
> 
> one tuple:
> {{}}
> {{{}}}
> {{{{}}}}
> {{{},{{}}}}
> ...
> 
> two tuples:
> {{},{{}}}
> {{{}},{{{}}}}
> {{},{{{}}}}
> ...
> 
> three tuples:
> {{},{{}},{{},{{}}}}
> {{},{{}},{{{}}}}
> ...
> 
> four tuples:
> {{},{{}},{{},{{}}},{{},{{}},{{},{{}}}}}
> etc.
> 
> ...

Thanks for the formalism suggestions, will try to absorb.

I know you've tried to explain various flavours of this to me before, 
but an example that prompts this for me, only with two attributes, is:

R2: {A integer, B typeof R2}

In R2, I can see that a value for B isn't necessarily empty, but if it 
is, that must be the end of the "descent", for I don't see how an empty 
recursive relation can recurse "any further" as it were.  (I think this 
would be the case even if R2 defined several "levels" of conventional 
non-recursive RVA's.)

Now, I admit I'm slow (but not heavy!) but I can see only one possible 
value for R.A which is an empty relation of type R and two possible 
values for R, one where R is empty and the other where R has one tuple 
where R.A is empty.  I don't see how a relation defined recursively can 
"descend" from an empty value!

So far, it looks like a peculiar kind of constraint to me.  As somebody 
else say, go ahead and attack it, I can take it!